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This study presents a rigorous investigation into the mathematical and physical properties inherent in the Fourier phase spectrum of earthquake ground motions. This exploration includes a detailed examination of the probability distribution of phase angles and differences, elucidated through two novel numerical experiments utilizing the reduction ad absurdum approach. Moreover, the study scrutinizes the physical attributes of earthquake ground motion's phase spectrum, employing the circular frequency-dependent phase derivative as a key analytical factor. In a novel approach, the research delves into the relationship between circular frequency-dependent phase derivatives and Fourier amplitudes, shedding light on essential connections within earthquake phenomena, particularly addressing non-stationarity. Expanding the scope, the study comprehensively examines the influence of source, propagation path, and site on both the phase spectrum and accelerogram. Employing the control variate technique facilitates this analysis, providing valuable insights into the underlying physical mechanisms governing earthquake wave behavior. The findings highlight the temporal properties of the phase spectrum, attributing its complexity to the temporal heterogeneity in energy release during the fault rupture and dispersion of earthquake waves. This novel approach not only enhances the understanding of earthquake dynamics, but also underscores the significance of considering temporal variations in earthquake events. [ABSTRACT FROM AUTHOR]

Aquifer diffusivity is a basic physical parameter used in hydrogeological calculations and is important for the evaluation and rational utilization of water resources, pollution prevention, and wetland protection. In this study, with the assumptions of aquifer isotropy, i.e., no vertical flow and constant saturated aquifer thickness, by using the Fourier transform and convolution theorem, a 1D analytical solution of the phase spectrum for an unconfined aquifer system was derived, which subsequently led to a phase spectrum solution for aquifer diffusivity. To test the efficacy, the proposed method was applied to a study site in the middle reach of the Hutuo River in the North China Plain. The estimated aquifer diffusivity ranged from 1.9 × 103 to 4.9 × 104 m2/d, with a mean of 2.2 × 104 m2/d, which was consistent with the results obtained using power spectral analysis, pumping tests, and inverse numerical models. The phase spectral approach proposed in this paper can estimate the aquifer properties on a larger scale. If long time series of hydraulic heads are available, it can estimate hydrogeological parameters accurately and quickly. Considering the similarity of the linearized governing equations, it can also be applied to the river–aquifer system and the confined aquifer system. [ABSTRACT FROM AUTHOR]

This study presents a rigorous investigation into the mathematical and physical properties inherent in the Fourier phase spectrum of earthquake ground motions. This exploration includes a detailed examination of the probability distribution of phase angles and differences, elucidated through two novel numerical experiments utilizing the reduction ad absurdum approach. Moreover, the study scrutinizes the physical attributes of earthquake ground motion’s phase spectrum, employing the circular frequency-dependent phase derivative as a key analytical factor. In a novel approach, the research delves into the relationship between circular frequency-dependent phase derivatives and Fourier amplitudes, shedding light on essential connections within earthquake phenomena, particularly addressing non-stationarity. Expanding the scope, the study comprehensively examines the influence of source, propagation path, and site on both the phase spectrum and accelerogram. Employing the control variate technique facilitates this analysis, providing valuable insights into the underlying physical mechanisms governing earthquake wave behavior. The findings highlight the temporal properties of the phase spectrum, attributing its complexity to the temporal heterogeneity in energy release during the fault rupture and dispersion of earthquake waves. This novel approach not only enhances the understanding of earthquake dynamics, but also underscores the significance of considering temporal variations in earthquake events.

Benefited from the latest advances in deep learning, convolutional neural network (CNN)-based SAR target recognition has made an excellent breakthrough. However, the most previous works pay attention to improve accuracy but neglect the working process analysis of the CNN models. Here, feature extraction of CNN plays an important role in recognition task. Moreover, in image processing field, frequency analysis is a classical way, which can directly reflect the frequency components of images. In view of that, we provide a feature extraction analysis method of pre-trained CNN in frequency domain in this paper. There are two analytical perspectives, i.e. amplitude and phase spectrum. Firstly, we can observe direction and range of pass-frequency through amplitude spectrum of convolution kernels, which represents information of raw SAR image and feature map captured from the convolution layer. Secondly, phase spectrums of SAR images store contour information of targets. We can understand the role of contour information from raw SAR images and feature maps in recognition task by phase spectrum analysis. In experiment part, according to the proposed feature extraction analysis method, we discuss the working process of several pre-trained CNN models. To some extent, it explains why the joint CNN has strong robustness against speckle noise in SAR image target recognition task. In short, the proposed feature extraction analysis method can improve the transparency and credibility of pre-trained CNN used for SAR target recognition. [ABSTRACT FROM AUTHOR]

We have demonstrated both numerically and experimentally a 2D plasmonic metamaterial the unit cell of which comprised an Archimedean spiral with a C-shaped resonator. Such metasurface enables the excitation of spoof localized plasmon resonances (LPRs) in the terahertz frequency range, similar in properties to the familiar LPRs in the visible range. We have compared the thin-film sensing potentials of the fundamental and dark resonant modes supported by the metasurface in the range of 0.2–0.5 THz. Both the amplitude and phase transmission spectra have been studied. A sensitivity of 21.1%/RIU (78.7 GHz/RIU) and a figure of merit (FOM) of 14.4 RIU−1 have been achieved. The FOM and Q factor obtained from the phase transmission spectra were shown to be about twice higher than those obtained from the amplitude spectra. [ABSTRACT FROM AUTHOR]

• An object azimuth measurement method based on OAM phase spectrum under tilted irradiation condition is proposed. • We analyze the relationship between the measurement error caused by the beam oblique irradiation and the angle of tilt and propose an error compensation method. After error compensation, the average error is kept below 0.73° at all tilt angles. • A four-step phase-shifting method is used to measure the helical phase of a vortex beam. In optical remote sensing, a beam carrying orbital angular momentum can be used to identify the azimuth of an object. However, most of the studies reported currently require the beam to be illuminated vertically to the surface of the object, and the general case of tilted irradiation for the beam has not been fully discussed. In this paper, an object azimuth measurement method based on orbital angular momentum phase spectrum under tilted irradiation condition is proposed. We analyze the relationship between the measurement error caused by the beam oblique irradiation and the angle of tilt and propose an error compensation method. In the experiment, the orbital angular momentum phase spectrum of the Laguerre-Gaussian beam is obtained by a four-step phase-shifting method, and the error caused by tilt modulation is measured. After implementing the error compensation scheme, the maximum absolute error in azimuth measurement under tilted irradiation conditions is maintained within 2.15°. Across all tilt angles, the average absolute error remains below 0.73°. The method proposed in this paper has a certain reference value for expanding the practical application of orbital angular momentum beams in the field of remote sensing. [ABSTRACT FROM AUTHOR]

We have evaluated the characteristics of the guided modes of a coupled SPR-Waveguide (SPR-WG) configuration consisting of Prism-gold-Dielectric 1-Dielectric 2-analyte and then have compared it with the conventional SPR structures. The penetration depth, the magnetic field distribution profile, the amplitude and phase spectra in this sensor strongly depend on the thickness of the dielectric layers used and the refractive index of the sensing medium (ns). The value of the field penetration depth in the proposed sensor can be increased by changing ns. The results indicated that the penetration depth values for the refractive indices of 1.333 and 1.533 are 8 µm and 80 µm, respectively. In addition, it was found that the SPR-WG sensor provides the highest sensitivity (equivalent to 200 RIU−1) among all sensors at ns = 1.533. The results also showed that the proposed sensor has a high phase sensitivity compared to the conventional SPR sensor. Overall, by adjusting the geometry parameters and ns, these sensors can be used as a useful tool for extracting optical information from biological samples, including prokaryotic and eukaryotic cells. [ABSTRACT FROM AUTHOR]

Summary: The stress state of steel members is an important indicator in evaluating structural safety. The ultrasonic time‐of‐flight method of measuring the stress of steel members based on acoustoelastic theory has been fully developed. However, the time difference is hard to be measured. The present paper proposes a new method of measuring the uniaxial stress of steel members using the phase spectrum of the ultrasonic transverse wave. The effect of interference of the two wave components generated by shear‐wave birefringence under uniaxial stress is investigated. It is found that the derivative curve of the phase spectrum of the pulse‐echo comprising the two wave components reaches a maximum periodically, and the frequency corresponding to the maxima is sensitive to stress and relatively easy to be measured. On this basis, a theoretical formula for the measurement of the uniaxial stress of steel members based on the phase spectrum is derived. Results of calibration tests show a good linear relationship between the stress and the reciprocal of the first response frequency corresponding to the maximum of the derivative curve of the phase spectrum. The uniaxial stress can then be measured by obtaining the first response frequency of the phase spectrum of the in‐service structural steel member. In addition, the effects of the thickness of steel members and the sampling rate of the oscilloscope on the uniaxial stress measurement are investigated. The present paper also illustrates the correspondence between the amplitude spectrum method and phase spectrum method. [ABSTRACT FROM AUTHOR]

Turbulence coherence in mountainous areas necessitates meticulous evaluation due to the complex terrain blocking. This study focuses on the turbulence coherence of the non-uniform wind field in a canyon via the anemometers positioned along a bridge span. Based on a proposed multi-point clustering, two categories of strong winds impacted by a nearby ridge are identified. The turbulence coherence of the two strong winds is then investigated with an extra focus on the phase spectrum. Several complex coherence functions are extended from commonly employed real forms, including the simplified Krenk's formula proposed. The fitting results of them all suggest that parameters such as the decay factor of the two strong winds show a negative linear correlation with separation but their relationship with wind speed is not significant. For the phase spectrum, in addition to skew winds, the contribution of horizontal wind shear is first emphasized in the two strong winds with piecewise fittings. This paper also discusses single-point coherence between the along-wind and vertical turbulence components. It is found to be unusually positive in sign due to the influence of the local topography and a formula with a constant term is suggested that substantially improves the fitting compared to Solari's formula. • The turbulence coherence with different separations is studied in a non-uniform wind field. • The strong winds are classified by multi-point clustering of the orthogonal components. • The contributions of horizontal wind shear and skew wind to the phase spectrum are emphasized. • The single-point coherence between different turbulence components is investigated. [ABSTRACT FROM AUTHOR]

Prioritized processing of fearful compared to neutral faces has been proposed to result from evolutionary adaptation of the contrast sensitivity function (CSF) to the features of emotionally relevant faces and/or vice versa. However, it is unknown whether a stimulus merely has to feature the amplitude spectrum of a fearful face to be prioritized or whether the relevant spatial frequencies have to occur with specific phases and orientations. Prioritized processing is indexed by specific increases of Event‐Related Potentials (ERPs) of the EEG and occurs throughout different early processing stages, indexed by emotion‐related modulations of the P1, N170, and EPN. In this pre‐registered study, we manipulated phase and amplitude properties of the Fourier spectra of neutral and fearful faces to test the effect of phase coherence (PC, face vs. scramble) and orientation coherence (OC, original vs. rotational average) and their interactions with differential emotion processing. We found that differential emotion processing was not present at the level of P1 but strongly affected N170 and EPN. In both cases, intact phase coherence was required for enhanced processing of fearful faces. OC did not interact with emotion. While faces produced the typical N170 effect, we observed a reversed effect for scrambles. Additional exploratory independent component analysis (ICA) suggests that this reversal could signal a mismatch between an early "perceptual hypothesis" and feedback of configural information. In line with our expectations, fearful‐neutral differences for the N170 and EPN depend on configural information, i.e., recognizable faces. Human contrast sensitivity is optimally tuned to the frequency spectrum of emotional faces, suggesting that a primary visual feature analysis contributes to emotional face processing. We show that electrophysiological indices of threat processing in fearful faces require intact phase information in their spectra. Orientation information does not show significant effects. In the absence of intact phase information, mid‐latency effects are reversed, possibly indicating a mismatch between an early "perceptual hypothesis" and feedback of configural information. [ABSTRACT FROM AUTHOR]

The existing deep neural network speech enhancement methods ignore the importance of phase spectrum learning and cause the enhanced speech quality to be unsatisfactory. In view of this problem, a speech enhancement method based on convolutional recurrent network and non-local modules is proposed in the present study. By designing an encoder-decoder network, the time-domain representation of the speech signal is used as the input of the encoding end for deep feature extraction, so as to make full use of the amplitude information and phase information of the speech signal. Non-local modules are added to the convolutional layers of the encoder and decoder to extract key features of the speech sequence while suppressing useless features. A gated loop unit network is introduced to capture the timing correlation information between the speech sequences. The experimental results on the ST-CMDS Chinese speech dataset show that compared with the unprocessed noisy speech, the quality and intelligibility of the enhanced speech are improved by 61% and 7.93% on average. [ABSTRACT FROM AUTHOR]

With the improvement of people's security awareness, numerous monitoring equipment has been put into use, resulting in the explosive growth of surveillance video data. Key frame extraction technology is a paramount technology for improving video storage efficiency and enhancing the accuracy of video retrieval. It can extract key frame sets that can express video content from massive videos. However, the existing key frame extraction algorithms of surveillance video still have deficiencies, such as the destruction of image information integrity and the inability to extract key frames accurately. To this end, this paper proposes a key frame extraction algorithm of surveillance video based on quaternion Fourier saliency detection. Firstly, the algorithm used colors, and intensity features to perform quaternion Fourier transform on surveillance video sequences. Next, the phase spectrum of the quaternion Fourier transformed image was obtained, and he image visual saliency map was obtained according to the quaternion Fourier phase spectrum. Then, the image visual saliency map of two adjacent frames is used to characterize the change of target motion state. Finally, the frames that can accurately express the motion state of the target are selected as key frames. The experimental results show that the method proposed in this paper can accurately capture the changes of the local motion state of the target while maintaining the integrity of the image information. [ABSTRACT FROM AUTHOR]

In this article, phase of the Fourier transform (FT), which has observed to be a crucial component in image representation, is utilized for visual target tracking. The main aim of the proposed scheme is to reduce the computational complexity of cross-correlation-based matching frameworks. Normalized cross-correlation (NCC) function-based object tracker is converted to a phase minimization problem under the following assumption: In visual object tracking applications, if the frame rate is high, the moving object can be considered to have translational shifts in image domain in a small time window. Since the proposed tracking framework works in the Fourier domain, the translational shifts in the image space are converted to phase variations in the Fourier domain due to the "translational invariance" property of the FT. The proposed algorithm estimates the spatial target position based on the phase information of the target region. The proposed framework uses the ℓ 1 -norm and provides a computationally efficient solution for the tracking problem. Experimental studies indicate that the proposed phase-based technique obtain comparable results with baseline tracking algorithms which are computationally more complex. [ABSTRACT FROM AUTHOR]

We have demonstrated both numerically and experimentally a 2D plasmonic metamaterial the unit cell of which comprised an Archimedean spiral with a C-shaped resonator. Such metasurface enables the excitation of spoof localized plasmon resonances (LPRs) in the terahertz frequency range, similar in properties to the familiar LPRs in the visible range. We have compared the thin-film sensing potentials of the fundamental and dark resonant modes supported by the metasurface in the range of 0.2–0.5 THz. Both the amplitude and phase transmission spectra have been studied. A sensitivity of 21.1%/RIU (78.7 GHz/RIU) and a figure of merit (FOM) of 14.4 RIU−1 have been achieved. The FOM and Q factor obtained from the phase transmission spectra were shown to be about twice higher than those obtained from the amplitude spectra.

In the seismic reliability analysis of engineering structures, it is often necessary to adopt stochastic ground motions as inputs. However, the current methods used to generate stochastic samples, such as the spectral representation method, the spectral transfer method, the dynamic source method, the physical source method, and the comprehensive method, etc., are not very convincing since they do not contain the complete information of seismic occurrence and propagation. In this study, an improved finite-fault model for stochastic simulation of ground motions is proposed. Compared to existing stochastic finite-fault model, the improved model considers the propagation law of phase spectrum, local site effect, and the impact of wave velocity on the arrival time of seismic waves. Besides, identification and statistics of model parameters are carried out based on ground motion records. Reasonable samples of stochastic ground motions are then obtained. In addition, parameter sensitivity analysis is conducted to determine critical random variables, which reduces the complexity of stochastic simulation. Simulation results are compared with recorded accelerograms from the 1999 Chi-Chi earthquake. It is shown that the improved stochastic finite-fault model is reliable, and the acceleration response spectra of simulated samples are consistent with those of station records collected at various site classes and the design spectra. • An improved finite-fault model for stochastic simulation of ground motions is proposed. • Parameter sensitivity analysis is conducted to determine critical random variables of model. • Simulation results are compared with recorded accelerograms from the 1999 Chi-Chi earthquake. • Acceleration response spectra of simulated samples are consistent with those of station records and design spectra. [ABSTRACT FROM AUTHOR]

• A new acoustic signal processing method has been proposed to localize multiple leaks in water pipes. • It optimally identifies linear phase segments with different slopes indicating leak locations in the phase curve. • Two leaks close to each other in a field pipe have been successfully detected using the new method. Acoustic signals measured at either side of a leak have been widely used for locating leaks in buried water distribution pipes. Conventional acoustic leak localization techniques (e.g, cross-correlation) may only pick up the strongest leak when multiple leaks exist in the same pipe. In this paper, a new method based on a linear phase detector has been proposed to address this issue for leak detection in water pipes. The linear phase detector utilizes the phase curve between the leak signals measured at two sides of the leaks. It involves an inverse optimization process that optimally identifies linear phase segments in the phase curve. Multiple leaks can be identified by these linear phase segments with different slopes which are correlated with the leak locations. Field investigations have been carried out on a water pipe which is a part of the water distribution system in a busy city area. The field experimental results validated the proposed method with two leaks close to each other being successfully detected. [ABSTRACT FROM AUTHOR]

• A new method for plane stress measurement is developed. • Transverse and longitudinal waves are used for plane stress separation. • The analytical expressions of plane stress-acoustic relations are obtained. • The phase spectra of echo waves are used for phase velocity measurement. • The stress coefficients are calibrated with unidirectional compression test. The measurement and monitoring of plane stress is important for the safety, reinforcement and maintenance of steel structures. In this study, a new method for plane stress measurement was developed theoretically and experimentally. Based on transverse wave birefringence, we deduced the stress-acoustic relations for plane stress separation by introducing longitudinal waves to increase the number of equations. In signal processing, we used the phase spectra of echoes to measure the polarized transverse wave phase velocity difference and the longitudinal wave phase velocity. The processed steel plate was regarded as a slightly orthotropic component and five stress coefficients need to be determined. Experiments were conducted on a total of four specimens. Strain gauge method was applied to confirm the validity of the proposed method. The results show that the proposed method can realize the direct separation of plane stress and has good accuracy on the laboratory scale. [ABSTRACT FROM AUTHOR]